Atheism, Evolution, Skepticism

How old is the Earth? Radionuclides

Below is a list of radionuclides (radioactive elements). These are unstable elements that have a tendency to undergo radioactive decay. The list contains every known radionuclide with a half-life longer than 300 years. A half-life is the amount of time it takes for half of a quantity of radioactive material to decay. So, if we start with 1.0 kg of Carbon-14, then after one half life (5,730 years), 0.5 kg of Carbon-14 will remain (and 0.5 kg of the decay product: Nitrogen-14). After another half-life, one half of the remaining Carbon-14 will exist (0.25 kg), and so on. A radionuclide will decay to nearly nothing after about 20 half-lifes. After that amount of time, the amount of radionuclide will be 1 / 2^20 (about one millionth) of it’s original quantity.

The second column of the list says how long the half-life of the element is. The fourth and fifth columns show how many half-lifes would have occurred in 4.5 billion years (the scientific estimate of the age of the earth), and 6,000 years (the age of the earth according to young earth creationists).

(Note to readers: Some of the numbers contain an “E”. This is a scientific notation indicating that you need to move the decimal point to the right to read the value. For example, 7.70E+24 years means “move the decimal point 24 spaces to the right” resulting in a value of 7,700,000,000,000,000,000,000,000 years.)

There are 92 radionuclides on this chart, and they show an interesting pattern. A lot of the radionuclides with long half-lifes exist in nature, but none of the radionuclides with short half-lifes exist. Now, as I mentioned earlier, radionuclides who have existed for more than 20 half-lifes would decay out of existence (at least as far as our being able to detect them). If evolutionists are right in claiming the earth to be 4.5 billion years old, we would expect radionuclides experiencing 20+ half-lifes within 4.5 billion years to have disappeared. (The number of half-lifes within 4.5 billion years can be found in column 4.) Any with longer half-lifes would still be around – assuming they existed on earth in the first place. Looking back at the list, we can see that all long-lived radionuclides exist on earth, and radionuclides with 20+ half-lifes don’t exist on earth with some exceptions.

There are some short-lived radionuclides that can be found on earth which are produced — they are either decay products from long-lived radionuclides, or produced by some continual process. So, it is not surprising that they still exist even in a very old earth:

> Uranium 236 is produced in uranium ores by neutrons from other radioactives.
> Iodine 129 is produced from Tellurium 130 by cosmic-ray muons.
> Manganese 53 and Beryllium 10 are produced by cosmic-ray radiation hitting dust in the upper atmosphere.
> Trace quantities of Np-237 are actually found in nature due to transmutation reactions in uranium ores produced by the neutrons which are present.
> Carbon 14 is produced in the upper atmosphere by radiation from the sun.
> U-234 is a product of U-238 decay (which has a 4.5 billion year half-life).
> Th-230 is a product of U-234 decay.
> Ra-226 is a product of Th-230 decay.
> Cl-36 is produced by cosmic ray interactions with Argon

There is one element in the long list that isn’t continually produced, but has been found despite the fact that would undergo 20+ half-lifes in 4.5 billion years: Pu-244. It has a half-life of 81 million years (i.e. 56 half-lifes within 4.5 billion years).

Finding Plutonium 244. Its half life is 82 million years, so 4.55 billion years is 55 half lives. You might reasonably ask how come Plutonium 244 isn’t listed as no. The answer is that someone made a very serious effort to find it: their article is referenced below. Eighty five kilograms of molybdenum ore were chemically concentrated, and then the lot was tediously run through a mass spectrometer. The amount of Plutonium 244 they found, 10-14 grams, was so small that it would have averaged one single radioactive decay every six years. Clearly, they could not have detected this Plutonium 244 with a geiger counter. However, 55 half lives ago, it would have been about one kilogram of plutonium metal. That’s believable in 85 kilograms of metal ore.

Samarium 146’s half life is 103 million years, so 4.55 billion years is 44 half lives. This means that Samarium 146 could be 200 billion times rarer than Uranium 235, but could be a thousand times commoner than Plutonium 244. I predict that if anyone tries very very hard to find Samarium 146, they will succeed. Curium 247, at almost 300 half lives, is completely out of the question. (Link)

U-235, which appears right above the 20 half-life dividing line, would have gone through 6.39 half-lifes in 4.5 billion years – meaning would decay to 1.2% of the quantity that it existed 4.5 billion years ago. It currently composes only 0.720% of Uranium in nature. This fits well with the expectation that U-235 would be slightly uncommon.

If we assume that the earth is young, the scarcity (but existence) of Pu-244 is a bit peculiar. The young earth hypothesis does not rule out finding minute quantities of Pu-244, but the diminishing abundances of radionuclides as we move through the 1 billion year – 50 million year half-life radionuclides looks peculiar. If the earth was truly only 6,000 years old, it means God created Pu-244 in extremely minute quantities. Had God produced it in larger quantities – quantities comparible to any of the 36 longer-lived radionuclides – then it would be implausible that the earth was very old because it would require that implausibly large amounts of Pu-244 existed 4.5 billion years ago.

So, all the short-lived nuclides which exist on earth are created by some process. There are no short lived radionuclides which exist on earth which are not created by some process on earth. Yet, every long-lived radionuclide exists regardless of whether it is produced on earth or not. This is what we would expect if the earth was old. If the earth is young, we would be surprised by the degree to which this pattern matches the “old earth” hypothesis. Although this pattern is not explicitly ruled out by the young earth hypothesis, the pattern is a quite peculiar.

I chose to list all the radionuclides which have half-lifes of 300+ years for one reason: a half-life of 300 years is exactly 20 half-lifes on a planet that is 6,000 years old. Notice that none of the radionuclides between Nb-92 and Cf-249 exist on earth except for the radionuclides we’ve talked about. There are 43 short-lived radionuclides in that group. If any of them had been present on earth 6,000 years ago “when the earth was created”, they would still exist. But, none of them exist.

One prediction of the old-earth hypothesis is that radionuclides would reach equilibrium with their decay products. For example, Uranium-238 decays into Thorium-234, which decays into Protactinium-234, and so on through a number of different radioactive elements until it turns into Lead-206, which is stable. This is what the U-238 decay chain looks like (starting with Uranium-238 and ending with Lead-206):

This decay chain has the effect of causing radionuclides to exist in specific proportions to each other. In this case, the proportion of U-238 to U-234 is governed by this equation:

Since we know the half-life of U-234 and U-238, we can calculate this value:

Now, creationists might wonder if this equilibrium can be reached within 6,000 years. This equilibrium cannot be reached in a short amount of time. It takes about 10 half-lifes of the daughter element before they will reach the equilibrium point. 10 half-lifes of U-234 is 2.4 million years. So, the abundance of U-238 and U-234 could not reach equilibrium in 6,000 years.

Other radionuclides in the U-238 decay chain are relatively short lived, so they only exist in minute quantities. We do know that Radon-222 exists, which means that Radium-226 (another radionuclide in the U-238 decay chain) is decaying in significant quantities. Radon-222 is the gas that seeps into basements and causes cancer. The EPA says that it is the second leading cause of lung cancer in the US. The very fact that Radon-222 exists on earth supports the assertion that the entire U-238 decay chain is filled and that requires quite a bit of time (or a deity who creates the earth and radionuclides precisely at their equilibrium points). If the earth is truly 6,000 years old, it means God even created Radon-222, which seeps into basements and causes lung cancers. Maybe He really wanted to make it look authentically old, even if that means causing cancer.

We can also look at other decay products and make predictions about their abundance on earth. We know that U-238 decays through a series of intermediates until it becomes the stable element Lead-206. Since U-238 should’ve gone through about 1 half-life in 4.5 billion years, we can say that half of the original U-238 has become Lead-206. This means that the abundance of Lead-206 be equal to or greater than the amount of U-238 we currently find on earth. In other words, the abundance of Lead-206 which is currently on earth should be = ( the amount of Lead-206 originally on earth ) + ( the amount of Lead -206 that should exist from radioactive decay within 4.5 billion years ). While it is difficult to know how much Lead-206 originally existed on earth, this calculation provides us with an absolute minimum of Lead-206 that should exist. Is there anything here that breaks the old earth theory?

* U-238 (4.47E+09 year half-life) decays into Lead-206. In the lithosphere (the top 25 miles of the earth’s crust), U-238 exists in a ratio of 2.4 ppm (particles per million) and Pb-206 exists in a ratio of 3.3 ppm. Since U-238 has gone through about 1 half life since the formation of the earth, then 2.4 ppm of U-238 should have decayed into Pb-206. Our prediction is confirmed: the abundance of Pb-206 (3.3 ppm) is greater than 2.4 ppm. We can also use the information to put a maximum age on the earth. If Pb-206 exists at 3.3 ppm and U-238 exists at 2.4 ppm, then the U-238 could not have gone through more than 1.25 U-238 half-life, which is 5.6 billion years.
* Th-232 (12 ppm, 1.41E+10 year half-life; 0.32 half-life in 4.5 billion years) decays into Pb-208. Th-232 should’ve produced 3.0 ppm of Pb-208. Pb-208 exists in an abundance of 7.3 ppm.
* Lu-176 (0.013 ppm, 3.78E+10 year half-life; 0.12 half-life in 4.5 billion years) decays into Hf-176. Lu-176 should’ve produced 0.001 ppm of Hf-176. Hf -176 exists in an abundance of 0.17 ppm.
* K-40 (2.457 ppm, 1.28E+9 year half-life; 3.52 half-life in 4.5 billion years) decays into Ca-40 (90%) and Ar-40 (10%). K-40 should’ve produced 16.72 ppm decay products (15 ppm Ca-40, 1.7 ppm Ar-40). Ca-40 exists in an abundance of 39,000 ppm, Ar-40 exists in an abundance of 1.2 ppm. Argon, however, is a gas, and therefore, would escape from the lithosphere into the atmosphere, explaining its low levels there. Argon makes up approximately 1% of the earth’s atmosphere.
* U-235 (0.017 ppm, 7.04E+8 year half-life; 6.39 half-life in 4.5 billion years) decays into Pb-207. U-235 should’ve produced 1.42 ppm of Pb-207. Pb-207 exists in an abundance of 3.08 ppm.

In none of these cases is there insufficient decay product.

The conclusion of all this is that assuming the earth *really is* 4.5 billion years allows you to make amazingly accurate predictions about the radionuclides you’d find on earth and their abundances. If the earth is truly is 6,000 years old, it means God created the earth with radionuclide abundances at precise levels that would match values we’d expect of an old earth, and the fact that you can use the assumption of an old earth to predict abundances of these materials is just an amazing coincidence. (I just can’t help but be reminded of the Pope’s advice to Galileo: that he’s allowed to assume the earth goes around the sun for the purpose of calculating orbits, but he isn’t allowed to claim it’s actually true.)

AnswersInGenesis attempts to answer these types of geological problems for the young earth hypothesis. I found it particularly amusing how they constantly play the “believe God, not man” game. Example:

Superficially, Hayward amasses an impressive battery of arguments as to why the Bible can’t mean what it says. Perhaps the single most important lesson from his book is his strategy itself. Each of his attacks on the Word of God elevates some other ‘authority’, whether derived from geology, astronomy, secular history or theology, above the Bible. This approach is as old as the Garden of Eden. True knowledge begins with the Bible (Proverbs 1:7, Psalms 119:160; 138:2), and that is where we need to start. God was there when He created the world.
– http://www.answersingenesis.org/docs/4127.asp

The only foolproof method for determining the age of something is based on eyewitness reports and a written record. We have both in the Bible. And that is why creationists use the historical evidence in the Bible to constrain their interpretations of the geological evidence.
– http://www.answersingenesis.org/creation/v24/i4/radiometric.asp

I find these answers to be particularly anti-intellectual, and disturbingly flexible. According to their argument, anything that contradicts the Bible is a-priori wrong. Now please disconnect your brains.

Ken Miller has a good discussion of this in his book Finding Darwin’s God. This is one of the things that a geologist showed him when he was wondering if there was something to all this Henry Morris stuff.

Of course, we should all remember the 100% best retort to the “how can you know that the world is old: WERE YOU THERE?”

Just respond: “Actually, yes I was there. How can you claim I wasn’t? WERE YOU THERE?!”

Actually, every element for which there is a “no” has a strong chance that they are a “yes” as well; the “yes” depends on how much of the element was present when the Earth was formed/created/whatever. Note that the events you apply to the finding of Sm146 could be applied (albeit not easily) to any of the other unstable isotopes further down the list. Consider how long the earth must age before all U-238 is gone; the number depends on how much U-238 was present when the Earth was born. Since the number of atoms is countable, the half-life sequence is not infinite, but is countable too and exceptionally long.

Consider the fallacy in attempting to determine the age of the Earth using radioactive isotopes — for example, measuring the ratio of U-238 and Pb-206 won’t work if lots of Pb-206 was already present in the materials used to build the Earth. In fact, we can’t even use the result to determine the age of the Universe — because we don’t know the sequence of the star/stars which (according to cosmologists) constructed the heavy elements (by heavy I mean heavier than helium) used in building the Earth, which star must of necessity not be our Sun (which has not yet aged enough in its sequence to begin building heavy elements).

Now, if I were a fundamentalist, I could say that God gets to make whatever God wants in creating the earth, and could make the earth seem older or younger than it actually is by adjusting the isotopes appropriately. Hence, the Earth could indeed be 6,000 years old, with isotope arrangements making it seem to be much older.

Since all we are dealing with is conjecture and theory, as “Bad” so adroitly points out, with one side using relative quantities of isotopes and the other side using a conversation with a being who claims to have participated in making this Universe, where are we?

Actually, every element for which there is a “no” has a strong chance that they are a “yes” as well; the “yes” depends on how much of the element was present when the Earth was formed/created/whatever. Note that the events you apply to the finding of Sm146 could be applied (albeit not easily) to any of the other unstable isotopes further down the list. Consider how long the earth must age before all U-238 is gone; the number depends on how much U-238 was present when the Earth was born. Since the number of atoms is countable, the half-life sequence is not infinite, but is countable too and exceptionally long.

I think you’re arguing that radioactive decay cannot completely eliminate the isotope from the earth, since it only halves it each half-life. However, if you have a large number of half-lifes, you can actually end up with 0. Here’s an example: let’s say that we have an earth-sized mass of Hf-182. The mass of the earth is 6×10^24 kg, and Avogadro’s number tells us that 182 kg of Hf-182 is 6.02 x 10^23 atoms. So, an earth-sized ball of Hf-182 contains ( 6.02 x 10^23 * 6 x 10^24 / 182 ) = 1.98 x 10^46 atoms. Now the calculation that tells us the amount of a radioactive element after time X is: ( initial amount ) / ( 2^number of half-lifes ). Our initial amount is 1.98 x 10^46 atoms. After 1 half lifes, our amount left is: 1.98 x 10^46 atoms / ( 2^1 ), which is 1 x 10^46 atoms. After 154 half-lifes, we have 1.98 x 10^46 atoms / 2.28 x 10^46. This is slightly less than one atom left on this earth-sized mass. Every half-life after this halves the atom’s chance of “survival”. What this means, then, is that it is possible for radioactive elements to decay to nothing. By the way, Hf-182, has gone through 500 half-lifes after 4.5 billion years, and it’s among the longer living non-existent radionuclides. It’s safe to say that none of the original Hf-182 is still around (although, I suppose there’s always the possibility of trace amounts arriving via meteor or something).

Consider the fallacy in attempting to determine the age of the Earth using radioactive isotopes — for example, measuring the ratio of U-238 and Pb-206 won’t work if lots of Pb-206 was already present in the materials used to build the Earth.

Yes, but we can still do lots of interesting stuff with the numbers – like put maximum ages on things. It’s possible that some of these numbers could’ve come out as: the earth could be no older than 10 thousand or 10 million years old. Also, if there are lots and lots of radionucleotides, and if the earth is truly young, then the odds all of them would end up not contradicting an old-earth becomes very unlikely – unless there is some deliberate deception at work.

Now, if I were a fundamentalist, I could say that God gets to make whatever God wants in creating the earth, and could make the earth seem older or younger than it actually is by adjusting the isotopes appropriately. Hence, the Earth could indeed be 6,000 years old, with isotope arrangements making it seem to be much older.

Yes, there’s no doubt that an all-powerful God could create the earth 6,000 years ago, or last night, and shape all evidence to the contrary, though that gets into some unseemly hints at a deceptive God.

[…] 2008 May 29, Thursday, 18:00 — monado Tiny Frog has a nice, detailed article analyzing the evidence from radionuclides about the age of the earth. The article compares what would be still on earth given its scientific age and if it were 6,000 […]

No significant progress in medicine and infectious disease occurred until somebody decided to ignore religious “truth” and establish scientific and factual “truth”.

It is fascinating that at least 1600 years A.D. of operating with religious truth did not produce the positive outcomes that < 400 years of scientific truth did, e.g. penicillin and chloroform.

Said another way, “Somebody’s lying”, either outright, or implicity.

One perturbing religious behavior is the willingness of large groups of people to delegate their deductive thinking to single individuals, who are, more often than not,poorly informed, self-appointed personalities perpetuating what they have been told ad infinitum.

Great post. I started to run through these same calculations myself (for the same purpose) when I came across your post. This saved me a lot of time.

My main disagreement with your write up is that isotopes should begin to decay as soon as they are formed rather than once the Earth was created. So wouldn’t your analysis show instead that the isotopes were probably formed 4.5 billion years ago, not that the Earth is 4.5 billion years old? Surely a lot of time passed between when they were formed in a supernova light years away to when the Earth was created.

My main disagreement with your write up is that isotopes should begin to decay as soon as they are formed rather than once the Earth was created. So wouldn’t your analysis show instead that the isotopes were probably formed 4.5 billion years ago, not that the Earth is 4.5 billion years old? Surely a lot of time passed between when they were formed in a supernova light years away to when the Earth was created.

Yes, that’s correct. I don’t know much about the time-gap that would need to happen between the death of the star (that produced the isotopes) and the formation of the solar system and earth. I’m also not sure if the supernova would need to be light years away. But, yes, you are correct.

Thanks James. I thought all were overlooking the obvious! It is pointless to try to refute the creationist answers using hard fact. It is simply a question of faith. Do we have more faith in science explaining through deduction how things came to be, or do we believe in an ancient text and all that goes with it?

Like the “many worlds” theorem, religeous explanations bring nothing to the table. They are not testable, offer no basis, and cannot be widened like scientific explanation to be tested. You either “believe” or you remain sceptical.

What James’ point introduces is the fact that the Earth’s constituents are 4.5bn year old, so the Earth can be _no_older_ than around 4.5bn years, but will be younger than this, perhaps be much younger than this. However, without the hand of God “laying it out already working” it cannot be anything like as young as 6,000 years.

There is a current mystery associated with the internal heat of the Earth. Why didn’t it all dissipate in the millenia before now?

I can only hazard a guess that the solution is that at the centre of the earth, (the core) far from being iron, is an enormous amount of highly radioactive matter.

This would explain how “new” material could arrive at the surface, that is as old as the Earth, or even newer, but is as old as 4.5bn years old itself. This would allow the Earth to be considerably older if there is sufficient convection in the interior to resurface minerals sufficiently. It could also explain how most of the earth is currently expanding and little is contracting, owing to phase changes within the raging core and mantle…

Someone sent me the link to this place, but I’m trying to figure these things out from square one, so to speak.

It’s one thing to give a chart saying this or that halflife is Xbillion years, but my question is where are you getting that number in the first place?

The only way I can envision those numbers appearing is by graphing known, verifiable data and extrapolating from there.

For example, lets say I found an old piece of paper. Based on my knowledge of what a 1 year old, 5 year old, and 10 year old piece of paper look like, I can judge by looking at the mystery paper how old it is. If it is within 10 years old, I can make a pretty good judgment. If it’s within 20 years old, I’m starting to speculate. And if it’s actually 1000 years old, how can I determine it’s age when all I have as a reference is 10 years old? The only possible explanation I can think of is that you are graphing the 1,5,10 points on a graph, drawing a ‘trend line’ of sorts, and then fitting the mystery paper to the graph and coming to a conclusion. The problem is the magnitudes are not comparable so that no actual trend line can be made, since on a scale of 0-1000 the data 1,5,10 effectively look like a single point. This is even more problematic if the graph takes on a non-linear trend and greater magnitudes than that.

If scientists have only been calculating half-lifes based on observing the decay over the last 100 years, how does that translate into ‘fact’ when taking that data back millions of years?

There’s a couple things. One way that half-lifes can be measured in the first place is to take a known quantity of a material (say 1 kilogram) and measure it’s decay over a period of time. If 1% of it decays in one year, that can be measured and extrapolated mathematically. There’s no reason to suppose that it somehow varies (unless it sets off a chain reaction, which most do not). Radiocarbon dating has been double-checked using old materials with known dates. For example, tree-ring data goes back thousands of years and wood can also be carbon-dated – allowing for comparisons of the two. They’ve also radiocarbon-dated materials found in Egyptian tombs with known historical dates, allowing for another verification.

It’s also my understanding that radioactive decay rates can be calculated mathematically using physics. This is one of the things that can be done with “physical chemistry”. We really know enough about subatomic particles to calculate decay rates mathematically.http://en.wikipedia.org/wiki/Physical_chemistry

I’m not suggesting they vary – though they very well could if we are only looking at less than 1% of earth’s history and assuming the the 99.999% of it remained in stable/constant conditions.

The ‘hang up’ for me is that as one extrapolates farther back into time, there is a very real uncertainty that must be accounted for. When you are comparing magnitudes of only 10, 50, 100, 1000 years, and for the sake of argument 10,000 years, when compared to 1 billion years that’s well below even 1% of earths total history.

Oh, I also forgot another piece of evidence that radioactive decay rates don’t vary – there’s a supernova that blew up, creating radioactive material in the process. Even though it blew up millions of years ago (the light it just reaching us now, for an event that happened a long time ago), the radioactive decay rate is at it’s predicted value.

I also think the physical processes behind radioactive decay are based on fundamental forces, which aren’t expected to vary. This is in contrast to say, the decay of larger materials like wood, which can fall apart at different rates based on things like humidity levels.

Also, the calculations of the uranium decay chain (in the post, and here: http://en.wikipedia.org/wiki/Decay_chain) shows something important about decay rates. Uranium decays through several different steps via different processes. They are alpha-decay (loss of Helium-4 from the nucleus; http://en.wikipedia.org/wiki/Alpha_decay) and beta-decay (loss of an electron; http://en.wikipedia.org/wiki/Beta_decay). If the decay rates changed over time, we would expect the alpha and beta decay rates to vary independently. But, if they did vary independently, it would cause the predicted ratio of uranium-decay elements to be different from the actual ratio. This would be detectable.

The fact that the uranium-decay product are at their predicted ratios means one of two things: either the decay rate hasn’t changed, or it means the decay rates both varied by the exact same multiple – which seems unlikely. (In other words, if one increased by 2x and the other increased by 2.4x, the percentages of the elements we see on earth would be different.)

I should also add that, if you speed-up radioactive decay, the planet also heats up. The only reason the interior of the earth is still molten is because of heat caused by radioactive decay. If that decay is speeded-up by a million fold (which would only compress 4.5 billion years into 4.5 thousand years – roughly the age of the earth as supposed by young earth creationists), there would be a lot of excess heat.

Because of quantum theory, elements give off light in very specific wavelengths. This allows us to determine the chemical composition of stars by looking at the light. (You can’t actually read the chemical composition with your eyes, you need specific instrument – a spectrometer, which shows exactly which frequencies of light are being given-off.) This is how we know, for example, that our sun is mostly composed of hydrogen and helium.

“spectral line
Light given off at a specific frequency by an atom or molecule. Every different type of atom or molecule gives off light at its own unique set of frequencies; thus, astronomers can look for gas containing a particular atom or molecule by tuning the telescope to one of the gas’s characteristic frequencies. For example, carbon monoxide (CO) has a spectral line at 115 Gigahertz (or a wavelength of 2.7 mm).”http://imagine.gsfc.nasa.gov/docs/dict_qz.html#spectral_line